Seminars

The superconformal indeces of 4d SCFTs count their BPS states and, holographically, give information on the microstates of the dual black holes. A possible approach to the exact computation of the index requires solving the so-called Bethe Ansatz equations (BAE). In this talk, I will introduce a rewriting of the BAE in terms of elliptic functions, focusing on the case with 16 supercharges. Such a rewriting permits 1) to quantitatively capture the conjectural relation of BAE with the Calogero-Moser integrable system (and the related continuous solutions) and 2) to rephrase the BAE in terms of configurations of lines on a plane intersecting an elliptic curve.

In this talk, I shall discuss about geometric properties of black hole horizons, both supersymmetric and non.
In the first part, I will focus on how string corrections affect properties of supersymmetric near-horizon geometries. I will consider whether there exists a doubling of the number of preserved supersymmetries, the so-called supersymmetry enhancement. Standard global theorems, such as the Lichnerowicz theorem, crucial to establish supersymmetry enhancement, will be presented. In the second part, I will consider the inverse problem of determining all black hole solutions associated to a prescribed near-horizon geometry. I will expand the horizon fields at first order in the radial coordinate, the so-called moduli, and show that the moduli must satisfy a system of elliptic PDEs, which implies that the moduli space is finite dimensional.
The talk is based on arXiv:1605.05635 [hep-th] and arXiv:1610.09949 [hep-th].

I will review some modern approaches to the analysis of supersymmetric field theories in (2+1)-dimensions with four supercharges. The presence of a CS action and of a Coulomb branch together with the absence of global anomalies and of a holographic dual description, have made the analysis of strong coupling complicated and only few aspects of these models have been investigated in the past. More recently, especially thanks to localization, many observable became accessible, boosting the number of non-perturbative and exact results.
I will review some of these new results, focusing on the role played by the one-loop exact partition function obtained by localization on the three sphere.

Generalized massless free theories can be consistently defined as CFTs. Their nearby Wilson-Fisher critical points can be studied using the analytic structure of generic conformal blocks. This way we obtain the leading order nontrivial anomalous dimensions and critical couplings for wide classes of theories, including generalized multicritical points, O(N) models and modes with multiple marginal deformations. Our results reveal an intriguing underlying structure in the web of generalized CFTs which is intimately connected to higher-spin theory.